Rigged arms changing volume
100% weight is not enough for ensuring a rigid stuck, check the deforming vertices: they surely have some weight relatively to another bone (shoulder, neck, head, ....). The vertices will move exactly with their bone if they're weighted to that bone ONLY (even if weight is not 100%).

So you have to remove unwanted weights.

Another method is to separate all pieces and parent them with the associated bone with the option Ctrl P - Bone.